RESUMEN

We present modeling and analysis of smectic C phases of liquid crystals capable of sustaining spontaneous polarization. The layered liquid crystals are also assumed to be chiral. We study minimization of the total energy subject to electrostatic constraints. In order to determine mathematically and physically relevant boundary conditions, we appeal to the analogy between the current problem and the vorticity in fluids. We place a special emphasis on the nonlocal and self-energy effects arising from spontaneous polarization. We discuss examples pertaining to the electric field created by the liquid crystal in dielectric medium, and also to the possible role of a domain shape as an energy reduction mechanism.

RESUMEN

Films and molds of nematic polymer materials are notorious for heterogeneity in the orientational distribution of the rigid rod or platelet macromolecules. Predictive tools for structure length scales generated by shear-dominated processing are vitally important: both during processing because of flow feedback phenomena such as shear thinning or thickening, and postprocessing since gradients in the rod or platelet ensemble translate to nonuniform composite properties and to residual stresses in the material. These issues motivate our analysis of two prototypes for planar shear processing: drag-driven Couette and pressure-driven Poiseuille flows. Hydrodynamic theories for high aspect ratio rod and platelet macromolecules in viscous solvents are well developed, which we apply in this paper to model the coupling between short-range excluded volume interactions, anisotropic distortional elasticity (unequal elasticity constants), wall anchoring conditions, and hydrodynamics. The goal of this paper is to generalize scaling properties of steady flow molecular structures in slow Couette flows with equal elasticity constants [M. G. Forest et al., J. Rheol., 48 (2004), pp. 175-192] in several ways: to contrast isotropic and anisotropic elasticity; to compare Couette versus Poiseuille flow; and to consider dynamics and stability of these steady states within the asymptotic model equations.